Oxygen can increase weight loss? Interesting. I live in an area with about 17% less oxygen than what is at sea level and we have the lowest obesity level in the country. Also, I'm no chemist, but I don't think the oxygen atom becomes unbonded from the two hydrogen atoms. Also the oxygen we breathe is O2, two oxygen atmos. I don't think 1 free oxygen atom is stable and would try to bond to something. But like I said, I'm no chemist so I can't remember for sure from my studies.
I drink, at minimum, 2 liters per day. More if I exercise or eat a lot of salty food. But I also live in a semi-arid climate that can get pretty hot during the summer, which was one of the caveats. I rarely drank water when I lived back east where it was cooler and more moist. I carry a bottle of water with me pretty much everywhere I go so that it's available to me when I need it. I also rely a lot more on lotions and chapsticks than I did before moving out here.
I guess I'm in the "drink when you feel you need to" camp, but I think having water at hand facilitates it.